Evaluate 6/7-2+-7/9+19/21
To evaluate the expression 6/7 - 2 + -7/9 + 19/21, we will follow the order of operations (PEMDAS/BODMAS) which states that we perform operations inside parentheses first (if any), then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Step 1: Simplify the numerator and denominator of each fraction individually.
Numerator of 6/7 = 6
Denominator of 6/7 = 7
Numerator of -7/9 = -7
Denominator of -7/9 = 9
Numerator of 19/21 = 19
Denominator of 19/21 = 21
Step 2: Apply operations in the order of operations.
6/7 - 2 + -7/9 + 19/21
Since there are no parentheses or exponents, we will move to multiplication and division from left to right.
6/7 - 2 + -7/9 + 19/21
There is no multiplication, so we move to division.
6/7 - 2 + -7/9 + 19/21
Next, we will do addition and subtraction from left to right.
6/7 - 2 + -7/9 + 19/21
= 0.8571 - 2 + -0.7778 + 0.9048
Now, we can add and subtract the values.
0.8571 - 2 + -0.7778 + 0.9048 = -1.016
Therefore, 6/7 - 2 + -7/9 + 19/21 equals approximately -1.016.
The common denominator is 63, so you have
54/63 - 126/63 - 49/63 + 57/63
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